Révision 563
Ajouté par Massamba FALL il y a presque 3 ans
| branch/fall_massamba/sp4a3/sp4a3_kalman.c | ||
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// Pour compiler : gcc sp4a3_kalman.c -lm
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include "sp4a3_kalman_extra.h"
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void Add_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
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}
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void Inverse_Mat_22(int n,int m,double A[n][m],double B[n][m]){
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}
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void Transpose_Mat(int n,int m,double A[n][m],double R[m][n]){
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int i,j;
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for (i=0;i<n;i++)
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for (j=0;j<m;j++)
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R[j][i]=A[i][j];
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}
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void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double R[na][ma]){
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}
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void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double R[na][mb]){
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}
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void tests_unitaires(void){
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//Matrices d'entrée
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double T21a[2][1]={{7},{-5}};
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double T21b[2][1]={{-3},{46}};
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double T22a[2][2]={{12,78},{-5,13}};
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double T22b[2][2]={{-25,36},{7,42}};
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double T24[2][4]={{7,-71,-12,3},{41,123,-5,10}};
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double T41a[4][1]={{45},{-123},{-78},{-410}};
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double T41b[4][1]={{-10},{45},{27},{-9}};
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double T42a[4][2]={{-73,45},{10,12},{-41,-35},{8,-23}};
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double T44a[4][4]={{1,2,7,4},{6,5,7,8},{9,8,7,6},{5,4,3,2}};
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double T44b[4][4]={{12,13,14,15},{21,22,23,40},{78,45,12,3},{54,10,12,47}};
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//Matrices résultat
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double R21[2][1],R22[2][2],R24[2][4],R41[4][1],R42[4][2],R44[4][4];
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//Matrices de validation
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double RST21[2][1]={{10},{-51}};
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double RInvT22[2][2]={{0.02380952380952381,-0.1428571428571428},{0.009157509157509158,0.02197802197802198}};
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double RAT22[2][2]={{-13,114},{2,55}};
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double RTT24[4][2]={{7,41},{-71,123},{-12,-5},{3,10}};
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double RMT24T41[2][1]={{8754},{-16994}};
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double RMT24T42[2][2]={{-705,-186},{-1478,3266}};
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double RMT24T44[2][4]={{-512,-425,-523,-606},{784,697,1143,1138}};
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double RAT41[4][1]={{35},{-78},{-51},{-419}};
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double RMT42T21[4][1]={{-736},{10},{-112},{171}};
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double RMT42T22[4][2]={{-1101,-5109},{60,936},{-317,-3653},{211,325}};
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double RMT42T24[4][4]={{1334,10718,651,231},{562,766,-180,150},{-1722,-1394,667,-473},{-887,-3397,19,-206}};
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double RTT44[4][4]={{1,6,9,5},{2,5,8,4},{7,7,7,3},{4,8,6,2}};
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double RMT44T41[4][1]={{-2387},{-4171},{-3585},{-1321}};
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double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};
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double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};
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double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};
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double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
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printf("Execution des tests unitaires.\n");
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Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition 2x4");
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Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");
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Inverse_Mat_22(2,2,T22a,R22); if (!Equal_Mat_Mat(RInvT22,R22)) error("Erreur calcul Inversion 2x2");
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Add_Mat_Mat(2,2,T22a,2,2,T22b,R22); if (!Equal_Mat_Mat(RAT22,R22)) error("Erreur calcul Addition 2x2");
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Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");
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Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");
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Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");
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Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");
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Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");
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Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");
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Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");
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Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");
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Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");
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Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calcul Multiplication 4x2 2x4");
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Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calcul Multiplication 2x4 4x1");
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Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calcul Multiplication 2x4 4x2");
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Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 2x4 4x4");
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printf("Test unitaires OK.\n");
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}
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int main(int argc,char **argv){
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tests_unitaires();
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FILE* fichier = fopen("pos_t_x_y.dat","r");
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if (fichier == NULL)
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error("Impossible d'ouvrir le fichier GPGGA_data.dat");
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FILE * Fout = Fout = fopen("output.dat","w");
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if (fichier == NULL)
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error("Impossible d'ouvrir le fichier output.dat");
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printf("Kalman\n");
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double t = 0;
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double t0,x0,y0;
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double xobs,yobs;
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double oldx,oldy;
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double dx=0,dy=0,dt=0.1;
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int cpt = 0;
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// kalman param
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double sigma_etat = 10.0;
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double sigma_observation = 2.0;
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double X[4][1] = {{0},{0},{0},{0}};
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double P[4][4] = {{sigma_etat*sigma_etat, 0, 0, 0},
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{0, sigma_etat*sigma_etat, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0, 0}};
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double Q[4][4] = {{0, 0, 0, 0},
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{0, 0, 0, 0},
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{0, 0, 0.1, 0},
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{0, 0, 0, 0.1}};
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double R[2][2] = {{sigma_observation*sigma_observation, 0},
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{0 , sigma_observation*sigma_observation}};
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double K[4][2];
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double H[2][4] = {{1, 0, 0, 0},
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{0, 1, 0, 0}};
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double HT[4][2];
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Transpose_Mat(2,4,H,HT);
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double F[4][4] = {{1, 0, dt, 0},
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{0, 1, 0, dt},
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{0, 0, 1, 0},
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{0, 0, 0, 1}};
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double FT[4][4];
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Transpose_Mat(4,4,F,FT);
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while(fscanf(fichier, "%lf %lf %lf", &t, &xobs, &yobs)>0){
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printf("-------------%04d--------------\n",cpt);
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if (cpt ==0)
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{
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t0=t;x0=xobs;y0=yobs;
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xobs=xobs-x0;yobs=yobs-y0;
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Plot_Mat(F,"F = ");
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Plot_Mat(H,"H = ");
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Plot_Mat(R,"R = ");
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}
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else
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{
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t -= t0;xobs -= x0;yobs -= y0;
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debug=0; ///Mettre à 1 pour afficher les matrices.
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///Ajouter votre code ci-dessous///
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// Kalman
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// X = F*X
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Plot_Mat(X," X(k+1|k) = ");
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//P = F*P*F'+Q;
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Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
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// K = P*H' / ( H*P*H' + R);
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Plot_Mat(K,"K = ");
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//X = X + K*([xobs(i);yobs(i)]-H*X);
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//Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k)");
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Plot_Mat(X," X(k+1|k+1) = X(k+1|k) + K.Delta = ");
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// P = P - K*H*P;
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Plot_Mat(P," P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
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/// La matrice X doit contenir la position filtrée ///
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}
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t = cpt * dt;
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dx = (xobs - oldx)/dt;
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dy = (yobs - oldy)/dt;
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fprintf(Fout,"%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n",t,xobs,yobs,sqrt(dx*dx+dy*dy)*dt,X[0][0],X[1][0],X[2][0],X[3][0],sqrt(X[2][0]*X[2][0]+X[3][0]*X[3][0])*dt);
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oldx = xobs;
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oldy = yobs;
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cpt ++;
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}
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fclose(Fout);
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fclose(fichier);
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system ("gnuplot -p -e \"plot 'output.dat' u 5:6 w l, '' u 2:3 w l\";");
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system ("gnuplot -p -e \"plot 'output.dat' u 1:9 w l, '' u 1:4 w l\";");
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system ("gnuplot -p -e \"plot 'output.dat' u 9 w l , 'vitesse_reelle.dat' u 2 w l\";");
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return 0;
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}
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// Pour compiler : gcc sp4a3_kalman.c -lm
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#include <stdlib.h>
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#include <stdio.h>
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#include <math.h>
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#include "sp4a3_kalman_extra.h"
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/* Transposer une matrice */
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void Transpose_Mat(int n, int m, double A[n][m], double R[m][n]){
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int i,j;
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for (i=0; i<n; i++)
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for (j=0; j<m; j++)
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R[j][i] = A[i][j];
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}
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/* Ajout de deux matrices */
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void Add_Mat_Mat(int na, int ma, double A[na][ma], int nb, int mb, double B[nb][mb], double out[na][ma])
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{
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// Vérifier que les matrices sont de la même taille. Sinon, renvoyer une erreur
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if (na != nb || ma != mb) error("(Add_Mat_Mat) ERREUR: Matrices de tailles differentes!\n");
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int i, j;
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for (i=0; i<na; i++)
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for (j=0; j<ma; j++)
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out[i][j] = A[i][j] + B[i][j];
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}
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/* Soustraction de matrice */
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void Sub_Mat_Mat(int na,int ma,double A[na][ma],int nb,int mb,double B[nb][mb], double out[na][ma])
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{
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// Vérifier que les matrices sont de la même taille, sinon renvoyer une erreur
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if (na != nb || ma != mb) error("(Sub_Mat_Mat) ERREUR: Matrices de tailles differentes!\n");
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int i,j;
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for (i=0; i<na; i++)
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for (j=0; j<ma; j++)
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out[i][j] = A[i][j] - B[i][j];
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}
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/* Inverser une matrice. ATTENTION : NE PAS FAIRE A = A^-1 */
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void Inverse_Mat_22(int n, int m, double A[n][m], double R[n][m])
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{
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double det = A[0][0]*A[1][1] - A[1][0]*A[0][1];
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// Si le déterminant est nul, la matrice est non inversible!!
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if (fabs(det) < 1e-15) error("ERREUR: Matrice non inversible\n");
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R[0][0] = 1.0/det * A[1][1];
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R[0][1] = -1.0/det * A[0][1];
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R[1][0] = -1.0/det * A[1][0];
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R[1][1] = 1.0/det * A[0][0];
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}
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/* Multiplication de matrices */
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void Mul_Mat_Mat(int na,int ma,double A[na][ma], int nb,int mb,double B[nb][mb], double out[na][mb])
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{
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// Vérifier que le nombre de colonnes de A = nombre de lignes de B
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if (ma != nb) error("ERREUR: ma n'est pas egal a nb\n");
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int i,j,k;
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double Rprime[na][mb]; // Matrice intermédiaire (cas où on fait A = A*B)
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// Initialiser tous les éléments de Rprime à 0
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for (i=0; i<na; i++)
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for (j=0; j<mb; j++)
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Rprime[i][j] = 0.0;
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// Faire le calcul et stocker dans la matrice intermédiaire
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for (i=0; i<na; i++)
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for (j=0; j<mb; j++)
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for (k=0; k<ma; k++)
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Rprime[i][j] += A[i][k] * B[k][j];
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// copier Rprime dans R
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for (i=0; i<na; i++)
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for (j=0; j<mb; j++)
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out[i][j] = Rprime[i][j];
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}
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/* Tests unitaires pour les opérations matricielles */
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void tests_unitaires(void){
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//Matrices d'entrée
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double T21a[2][1]={{7},{-5}};
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double T21b[2][1]={{-3},{46}};
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double T22a[2][2]={{12,78},{-5,13}};
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double T22b[2][2]={{-25,36},{7,42}};
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double T24[2][4]={{7,-71,-12,3},{41,123,-5,10}};
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double T41a[4][1]={{45},{-123},{-78},{-410}};
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double T41b[4][1]={{-10},{45},{27},{-9}};
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double T42a[4][2]={{-73,45},{10,12},{-41,-35},{8,-23}};
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double T44a[4][4]={{1,2,7,4},{6,5,7,8},{9,8,7,6},{5,4,3,2}};
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double T44b[4][4]={{12,13,14,15},{21,22,23,40},{78,45,12,3},{54,10,12,47}};
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//Matrices résultat
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double R21[2][1],R22[2][2],R24[2][4],R41[4][1],R42[4][2],R44[4][4];
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//Matrices de validation
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double RST21[2][1]={{10},{-51}};
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double RInvT22[2][2]={{0.02380952380952381,-0.1428571428571428},{0.009157509157509158,0.02197802197802198}};
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double RAT22[2][2]={{-13,114},{2,55}};
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double RTT24[4][2]={{7,41},{-71,123},{-12,-5},{3,10}};
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double RMT24T41[2][1]={{8754},{-16994}};
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double RMT24T42[2][2]={{-705,-186},{-1478,3266}};
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double RMT24T44[2][4]={{-512,-425,-523,-606},{784,697,1143,1138}};
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double RAT41[4][1]={{35},{-78},{-51},{-419}};
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double RMT42T21[4][1]={{-736},{10},{-112},{171}};
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double RMT42T22[4][2]={{-1101,-5109},{60,936},{-317,-3653},{211,325}};
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double RMT42T24[4][4]={{1334,10718,651,231},{562,766,-180,150},{-1722,-1394,667,-473},{-887,-3397,19,-206}};
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double RTT44[4][4]={{1,6,9,5},{2,5,8,4},{7,7,7,3},{4,8,6,2}};
|
||
|
double RMT44T41[4][1]={{-2387},{-4171},{-3585},{-1321}};
|
||
|
double RMT44T42[4][2]={{-308,-268},{-611,-99},{-816,118},{-432,122}};
|
||
|
double RAT44[4][4]={{13,15,21,19},{27,27,30,48},{87,53,19,9},{59,14,15,49}};
|
||
|
double RST44[4][4]={{-11,-11,-7,-11},{-15,-17,-16,-32},{-69,-37,-5,3},{-49,-6,-9,-45}};
|
||
|
double RMT44T44[4][4]={{816,412,192,304},{1155,583,379,687},{1146,668,466,758},{486,308,222,338}};
|
||
|
|
||
|
printf("Execution des tests unitaires.\n");
|
||
|
Transpose_Mat(2,4,T24,R42); if (!Equal_Mat_Mat(RTT24,R42)) error("Erreur calcul Transposition 2x4");
|
||
|
Transpose_Mat(4,4,T44a,R44); if (!Equal_Mat_Mat(RTT44,R44)) error("Erreur calcul Transposition 4x4");
|
||
|
Inverse_Mat_22(2,2,T22a,R22); if (!Equal_Mat_Mat(RInvT22,R22)) error("Erreur calcul Inversion 2x2");
|
||
|
Add_Mat_Mat(2,2,T22a,2,2,T22b,R22); if (!Equal_Mat_Mat(RAT22,R22)) error("Erreur calcul Addition 2x2");
|
||
|
Add_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RAT44,R44)) error("Erreur calcul Addition 4x4");
|
||
|
Add_Mat_Mat(4,1,T41a,4,1,T41b,R41); if (!Equal_Mat_Mat(RAT41,R41)) error("Erreur calcul Addition 4x1");
|
||
|
Sub_Mat_Mat(2,1,T21a,2,1,T21b,R21); if (!Equal_Mat_Mat(RST21,R21)) error("Erreur calcul Soustraction 2x1");
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||
|
Sub_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RST44,R44)) error("Erreur calcul Soustraction 4x4");
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||
|
Mul_Mat_Mat(4,4,T44a,4,4,T44b,R44); if (!Equal_Mat_Mat(RMT44T44,R44)) error("Erreur calcul Multiplication 4x4 4x4");
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||
|
Mul_Mat_Mat(4,4,T44a,4,1,T41a,R41); if (!Equal_Mat_Mat(RMT44T41,R41)) error("Erreur calcul Multiplication 4x4 4x1");
|
||
|
Mul_Mat_Mat(4,4,T44a,4,2,T42a,R42); if (!Equal_Mat_Mat(RMT44T42,R42)) error("Erreur calcul Multiplication 4x4 4x2");
|
||
|
Mul_Mat_Mat(4,2,T42a,2,1,T21a,R41); if (!Equal_Mat_Mat(RMT42T21,R41)) error("Erreur calcul Multiplication 4x2 2x1");
|
||
|
Mul_Mat_Mat(4,2,T42a,2,2,T22a,R42); if (!Equal_Mat_Mat(RMT42T22,R42)) error("Erreur calcul Multiplication 4x2 2x2");
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||
|
Mul_Mat_Mat(4,2,T42a,2,4,T24,R44); if (!Equal_Mat_Mat(RMT42T24,R44)) error("Erreur calcul Multiplication 4x2 2x4");
|
||
|
Mul_Mat_Mat(2,4,T24,4,1,T41a,R21); if (!Equal_Mat_Mat(RMT24T41,R21)) error("Erreur calcul Multiplication 2x4 4x1");
|
||
|
Mul_Mat_Mat(2,4,T24,4,2,T42a,R22); if (!Equal_Mat_Mat(RMT24T42,R22)) error("Erreur calcul Multiplication 2x4 4x2");
|
||
|
Mul_Mat_Mat(2,4,T24,4,4,T44a,R24); if (!Equal_Mat_Mat(RMT24T44,R24)) error("Erreur calcul Multiplication 2x4 4x4");
|
||
|
printf("Test unitaires OK.\n");
|
||
|
}
|
||
|
|
||
|
// ============================================= MAIN =====================================================================
|
||
|
|
||
|
int main(int argc,char **argv){
|
||
|
|
||
|
tests_unitaires();
|
||
|
|
||
|
FILE* fichier = fopen("pos_t_x_y.dat","r");
|
||
|
if (fichier == NULL)
|
||
|
error("Impossible d'ouvrir le fichier GPGGA_data.dat");
|
||
|
|
||
|
FILE * Fout = fopen("output.dat","w");
|
||
|
if (fichier == NULL)
|
||
|
error("Impossible d'ouvrir le fichier output.dat");
|
||
|
|
||
|
printf("Kalman\n");
|
||
|
double t = 0;
|
||
|
double t0,x0,y0;
|
||
|
double x,y;
|
||
|
double oldx,oldy;
|
||
|
double dx=0,dy=0,dt=0.1;
|
||
|
int cpt = 0;
|
||
|
|
||
|
// kalman param
|
||
|
double sigma_etat = 10.0;
|
||
|
double sigma_observation = 2.0;
|
||
|
double X[4][1] = {{0},{0},{0},{0}};
|
||
|
|
||
|
double P[4][4] = {{sigma_etat*sigma_etat, 0, 0, 0},
|
||
|
{0, sigma_etat*sigma_etat, 0, 0},
|
||
|
{0, 0, 0, 0},
|
||
|
{0, 0, 0, 0}};
|
||
|
|
||
|
double Q[4][4] = {{0, 0, 0, 0},
|
||
|
{0, 0, 0, 0},
|
||
|
{0, 0, 0.1, 0},
|
||
|
{0, 0, 0, 0.1}};
|
||
|
|
||
|
double R[2][2] = {{sigma_observation*sigma_observation, 0},
|
||
|
{0 , sigma_observation*sigma_observation}};
|
||
|
|
||
|
double K[4][2];
|
||
|
double H[2][4] = {{1, 0, 0, 0},
|
||
|
{0, 1, 0, 0}};
|
||
|
double HT[4][2];
|
||
|
Transpose_Mat(2,4,H,HT);
|
||
|
|
||
|
double F[4][4] = {{1, 0, dt, 0},
|
||
|
{0, 1, 0, dt},
|
||
|
{0, 0, 1, 0},
|
||
|
{0, 0, 0, 1}};
|
||
|
double FT[4][4];
|
||
|
Transpose_Mat(4,4,F,FT);
|
||
|
|
||
|
while(fscanf(fichier, "%lf %lf %lf", &t, &x, &y)>0){
|
||
|
printf("-------------%04d--------------\n",cpt);
|
||
|
|
||
|
if (cpt ==0)
|
||
|
{
|
||
|
t0=t;x0=x;y0=y;
|
||
|
x=x-x0;y=y-y0;
|
||
|
Plot_Mat(F,"F = ");
|
||
|
Plot_Mat(H,"H = ");
|
||
|
Plot_Mat(R,"R = ");
|
||
|
}
|
||
|
else
|
||
|
{
|
||
|
t -= t0;x -= x0;y -= y0;
|
||
|
|
||
|
debug=0; //Mettre à 1 pour afficher les matrices.
|
||
|
//Ajouter votre code ci-dessous//
|
||
|
// Kalman
|
||
|
|
||
|
/** ETAPE 1 : Prédiction **/
|
||
|
//X = F*X
|
||
|
Plot_Mat(X," X(k|k) = ");
|
||
|
Mul_Mat_Mat(4, 4, F, 4, 1, X, X);
|
||
|
Plot_Mat(X," X(k+1|k) = ");
|
||
|
|
||
|
//P = F*P*F'+Q;
|
||
|
double Ftemp[4][4], Atemp[4][2], Btemp[2][2], Ctemp[2][2]; // Variables intermédiaires pour calculs
|
||
|
Plot_Mat(P,"P(k|k) = ");
|
||
|
Mul_Mat_Mat(4, 4, F, 4, 4, P, Ftemp); // Ftemp = F*P
|
||
|
Mul_Mat_Mat(4, 4, Ftemp, 4, 4, FT, Ftemp); // Ftemp = Ftemp*FT = F*P*FT
|
||
|
Add_Mat_Mat(4, 4, Ftemp, 4, 4, Q, P); // P = Ftemp + Q = F*P*FT + Q
|
||
|
Plot_Mat(P,"P(k+1|k) = F.P(k|k).FT + Q = ");
|
||
|
|
||
|
/** ETAPE 2 : GAIN **/
|
||
|
// K = P*H' / ( H*P*H' + R);
|
||
|
Mul_Mat_Mat(4, 4, P, 4, 2, HT, Atemp); // Atemp = P*HT
|
||
|
Plot_Mat(Atemp, "P(k+1|k).HT = ");
|
||
|
|
||
|
Mul_Mat_Mat(2, 4, H, 4, 2, Atemp, Atemp); // Atemp = H*Atemp = H*P*HT
|
||
|
Add_Mat_Mat(2, 2, Atemp, 2, 2, R, Atemp); // Atemp = Atemp + R = H*P*HT + R
|
||
|
Plot_Mat(Btemp,"H.P(k+1|k).HT + R = ");
|
||
|
Inverse_Mat_22(2, 2, Atemp, Btemp); // Btemp = Atemp^-1 = (H*P*HT + R)^-1
|
||
|
Plot_Mat(Btemp,"INV(H.P(k+1|k).HT + R) = ");
|
||
|
Mul_Mat_Mat(4, 4, P, 4, 2, HT, Ctemp); // Ctemp = P*HT
|
||
|
Mul_Mat_Mat(4, 2, Ctemp, 2, 2, Btemp, K); // K = Ctemp * Btemp = P*HT * (H*P*HT + R)^-1
|
||
|
Plot_Mat(K,"K = ");
|
||
|
|
||
|
/** ETAPE 3 : Mise à jour **/
|
||
|
//X = X + K*([xb(i);yb(i)]-H*X);
|
||
|
double Delta[2][1];
|
||
|
double Obs[2][1] = {{x}, {y}};
|
||
|
Plot_Mat(Obs, "Obs = ");
|
||
|
|
||
|
// Calcul du delta
|
||
|
double Ytemp[2][4];
|
||
|
Mul_Mat_Mat(2, 4, H, 4, 1, X, Ytemp); // Ytemp = H*X
|
||
|
Sub_Mat_Mat(2, 1, Obs, 2, 1, Ytemp, Delta); // Delta = Obs - Ytemp = Obs - H*X
|
||
|
Plot_Mat(Delta,"DELTA = Obs - H.X(k+1|k) = ");
|
||
|
|
||
|
// Calcul de X
|
||
|
double Ztemp[4][1];
|
||
|
Mul_Mat_Mat(4, 2, K, 2, 1, Delta, Ztemp); // Ztemp = K*Delta
|
||
|
Add_Mat_Mat(4, 1, X, 4, 1, Ztemp, X); // X = X + Ztemp = X + K*Delta
|
||
|
Plot_Mat(X,"X(k+1|k+1) = X(k+1|k) + K.Delta = ");
|
||
|
|
||
|
// P = P - K*H*P;
|
||
|
double Htemp[4][4], Gtemp[4][4];
|
||
|
Mul_Mat_Mat(4, 2, K, 2, 4, H, Htemp); // Htemp = K*H
|
||
|
Plot_Mat(Htemp,"K.H = ");
|
||
|
Mul_Mat_Mat(4, 4, Htemp, 4, 4, P, Gtemp); // Gtemp = Htemp * P = K*H*P
|
||
|
Plot_Mat(Gtemp,"K.H.P = ");
|
||
|
Sub_Mat_Mat(4, 4, P, 4, 4, Gtemp, P); // P = P - Gtemp = P - K*H*P
|
||
|
Plot_Mat(P,"P(k+1|k+1) = P(k+1|k) - K.H.P(k+1|k) = ");
|
||
|
|
||
|
/// La matrice X doit contenir la position filtrée ///
|
||
|
}
|
||
|
t = cpt * dt;
|
||
|
dx = (x - oldx)/dt;
|
||
|
dy = (y - oldy)/dt;
|
||
|
fprintf(Fout,"%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\t%f\n",t,x,y,sqrt(dx*dx+dy*dy)*dt,X[0][0],X[1][0],X[2][0],X[3][0],sqrt(X[2][0]*X[2][0]+X[3][0]*X[3][0])*dt);
|
||
|
oldx = x;
|
||
|
oldy = y;
|
||
|
cpt ++;
|
||
|
}
|
||
|
fclose(Fout);
|
||
|
fclose(fichier);
|
||
|
|
||
|
system ("gnuplot -p -e \"plot 'output.dat' u 5:6 w l, '' u 2:3 w l\";");
|
||
|
system ("gnuplot -p -e \"plot 'output.dat' u 1:9 w l, '' u 1:4 w l\";");
|
||
|
system ("gnuplot -p -e \"plot 'vitesse_reelle.dat' u 2 w l, 'output.dat' u 9 w l\";");
|
||
|
return 0;
|
||
|
}
|
||
Formats disponibles : Unified diff
Aprés quelques heures de bataille, mission accomplie, le filtre de KALMAN fonctionne très très très très bien .VAMOSSSSSSSSSSSSSSSSS